A salient feature of anthropogenic climate change is the enhanced warming of the tropical Indian Ocean (TIO) relative to the tropics. Recent studies show that this warming can remotely modulate the Atlantic meridional overturning circulation (AMOC). Motivated by these results, we systematically study the sensitivity of the AMOC and Atlantic climate to changes in TIO temperature using the latest coupled climate model from the Institut Pierre Simon Laplace (IPSL-CM6A-LR). Ensemble experiments nudging the TIO surface temperatures by-2°C,-1°C, +1°C, and +2°C are conducted. Within a few years after the forcing is imposed, different atmospheric teleconnections begin to drive the AMOC "fast" and "slow" responses, yielding after 150 years an AMOC equilibrium sensitivity of about +9.4 Sv per 1°C of relative TIO warming. A water mass transformation analysis shows that the fast response to TIO warming (on decadal timescales) is largely driven by surface cooling in the Labrador Sea caused by an induced positive North Atlantic Oscillation (NAO)-like mean pattern. By contrast, the slow response (on multi-decadal to centennial timescales) is driven by the gradual advection of positive salinity anomalies from the tropical Atlantic, which predominantly affect the Nordic Seas. The response is non-linear in that a TIO warming strengthens the AMOC through increase in Labrador Sea deep water formation, while a TIO cooling slows down the AMOC via sea ice expansion over the Nordic Seas deep-water formation region, ultimately leading to the AMOC shutdown in the-2ºC-TIO experiment. These results help understand the role of interbasin connections and AMOC drivers in a warming climate.